Шыныбеков А.Н. Алгебра 9-сынып, 2013

Review of Grade 8 material

1.1. Equations in two variables

1.2. Geometric meaning of equations in two variables

2.1. Methods for solving systems of linear equations

2.2. Solving systems of second-degree equations

3. Problems solved by forming systems of equations

4.1. Concept of solving inequalities

4.2. Solving systems of inequalities in one variable

Additional problems for Chapter 1

2.1. Definition of a numerical sequence

2.2. Methods of defining a numerical sequence

2.3. Monotone sequences

2.4. Principle of mathematical induction

2.5. Concept of an arithmetic progression

2.6. Formula for the nth term of an arithmetic progression

2.7. Concept of a geometric progression

2.8. Formula for the nth term of a geometric progression

2.9. Formulas for sums of the first n terms of arithmetic and geometric progressions

2.10. Sum of the first n terms of an arithmetic progression

2.11. Sum of the first n terms of a geometric progression

2.12. Concept of the limit of a numerical sequence

2.13. Definition of the limit of a numerical sequence

2.14. Basic properties of limits

2.15. Limit of a bounded monotone sequence

2.16. Concept of a numerical series. Sum of an infinite decreasing geometric progression

2.17. Concept of a numerical series

2.18. Infinite decreasing geometric progression

2.19. Converting repeating decimals to common fractions

Additional problems for Chapter 2

3.1. Angles and arcs

3.2. Radian measure of an angle

3.3. Definition of trigonometric functions

3.4. Definition of trigonometric functions for arbitrary angles

3.5. Values of trigonometric functions for selected angles

3.6. Properties of trigonometric functions

3.7. Signs of trigonometric functions

3.8. Evenness and oddness of trigonometric functions

3.9. Periodicity of trigonometric functions

3.10. Reduction formulas

3.11. Transforming trigonometric expressions and proving identities

3.12. Addition formulas

3.13. Double-angle and half-angle formulas

3.14. Double-angle formulas

3.15. Half-angle formulas

3.16. Formulas for converting sums and differences of trigonometric functions to products and products to sums

3.17. Converting sums and differences to products

3.18. Converting products to sums

Additional problems for Chapter 3

4.1. Sample space

4.2. Operations on events

4.3. Probability of an event and its properties

4.4. Classical definition of probability

4.5. Properties of probability

4.6. Geometric probability

4.7. Elements of combinatorics

4.8. Addition rule

4.9. Multiplication rule

4.10. Arrangements with repetition

4.11. Arrangements without repetition. Permutations

4.12. Combinations without repetition

4.13. Applying combinatorial formulas to calculate event probabilities

4.14. Statistical characteristics

Additional problems for Chapter 4

Review exercises for Grades 7–9

Natural numbers and integers. Divisibility of numbers

Rational and irrational numbers. Square roots

Special product formulas

Quadratic equation. Vieta's theorem

Polynomials and their roots

Equations and systems of equations

Proving inequalities

Solving inequalities. Interval method

Powers with integer and rational exponents

Analyzing a function and plotting its graph

Numerical sequences. Arithmetic and geometric progressions

Trigonometric expressions

Answers